This follow-up shows a lot of maturity. Both sides are obviously at fault here, although you instigated it.
I suspect you could still get the internship if you send an apology like "Sorry for my previous emails they were out of line. You're essentially correct and here's an updated resume to reflect that."
I suspect you could still get the internship if you send an apology like "Sorry for my previous emails they were out of line. You're essentially correct and here's an updated resume to reflect that."